Throwing spatial light: on topological explanations in Gestalt psychology

Abstract

It is a well-known fact that mathematics plays a crucial role in physics; in fact, it is virtually impossible to imagine contemporary physics without it. But it is questionable whether mathematical concepts could ever play such a role in psychology or philosophy. In this paper, we set out to examine a rather unobvious example of the application of topology, in the form of the theory of persons proposed by Kurt Lewin in his Principles of Topological Psychology. Our aim is to show that this branch of mathematics can furnish a natural conceptual system for Gestalt psychology, in that it provides effective tools for describing global qualitative aspects of the latter’s object of investigation. We distinguish three possible ways in which mathematics can contribute to this: explanation, explication (construed in the spirit of Carnap) and metaphor. We hold that all three of these can be usefully characterized as throwing light on their subject matter, and argue that in each case this contrasts with the role of explanations in physics. Mathematics itself, we argue, provides something different from such explanations when applied in the field of psychology, and this is nevertheless still cognitively fruitful.

Towards a topological philosophy

“…For example, Skowron and Wójtowicz 2021 presents a discussion of Lewin's topologization of the structure of persons that could be regarded as constituting the first step towards a topologization of the mind. Let us assume, for the purposes of this article, that we construe the mind in broad terms—that is, more or less as Lewin (1936) understood the person.…”

“…One can also claim that it is possible to throw topological light on philosophical issues . (This formulation is introduced and analyzed in Skowron and Wójtowicz 2021 when discussing applications of topological notions in Gestalt psychology.) Marshall Stone's motto “You Must Always Topologize” (cf.…”

A metaphysical foundation for mathematical philosophy

“…One might say that philosophical findings count as illuminating if and when they shed new light on problems, opening up some novel perspective or other that significantly broadens our understanding. Consider two conceptual realms (see Skowron & Wójtowicz, 2021): a philosophical one P and a mathematical one M (where the latter could be any branch of mathematics). A mathematical philosopher starts with P, then notes certain similarities between P and M (based on common ideas), and, on that basis, constructs a mapping Φ:P→M.…”

“…It is reported that Gödel considered Husserl the greatest philosopher since Leibniz (Rota, 1992, p. 175). Phenomenology and mathematics were, and still are, connected by many threads-a fact to which many works testify (see Tieszen, 1995Tieszen, , 2005Fine, 1995;Berghofer, 2020;Hartimo, 2007Hartimo, , 2010Skowron & Wójtowicz, 2021). In order to achieve our goal, we shall therefore adopt the phenomenological approach as proposed by Husserl and substantially developed by his pupil Ingarden.…”

Application of Cognitive System Model and Gestalt Psychology in Residential Healthy Environment Design

“…It is based on the above research conclusions, in order to improve the environmental comfort of the residential area, this paper introduces the psychological theory into the environmental design of the residential area. Typical psychological theories mainly include cognitive system model and Gestalt psychology [ 11 – 13 ], color psychology [ 14 – 16 ], cognitive psychology [ 17 – 19 ], ecological self-consciousness theory [ 20 ], and probability self-consciousness theory [ 21 ]. Gestalt psychology is most widely and successfully used in interaction design.…”